a-rocket-is-launched-into-the-air-a-few-moments-after-lifterf-the-rocket-is-40-mathrmm-above-the-gro

Question

A rocket is launched into the air. A few moments after lifterf, the
rocket is 40 $\mathrm{m}$ above the ground. After another 5 $\mathrm{s}$ , the rocket is now aoo $\mathrm{m}$ off the ground. What is the average velocity of the rocket during the 5 s part of the flight?
(A) 16 $\mathrm{m} / \mathrm{s}$
(B) 32 $\mathrm{m} / \mathrm{s}$
(C) 48 $\mathrm{m} / \mathrm{s}$
(D) 64 $\mathrm{m} / \mathrm{s}$

Salamat Ali · Accepted Answer

the original Lost in the rocket is given by rate of change of displacement, Celtics or delta T. So changing displacement we have here 200 minus minus 14 5 seconds. Five seconds. So are ever jewel lost. Four up. It is it that you do meet it per second for a second. So Option D&#x27;s option bees, Right? End off the problem. Thank you for watching.

Emily Reynolds · Answer

okay, in this question, we have a rocket that is going up, and then it runs out of fuel, and then it&#x27;s gonna ultimately come back down to the ground. Okay, so it tells us that it travels, um, 1200 meters before it runs out of fuel. The initial velocity is zero meters per second, and we&#x27;re trying to figure out the final velocity when it runs out of fuel. And it also tells us that, um, while the rocket is accelerating, has an acceleration of 3.2 meters per second squared. Okay, So to figure out this first portion, I&#x27;m gonna use this formula. VF squared equals V. I squared, plus two a Delta X. Now my VF squared is what I don&#x27;t know. Nero plus to times 3.2 times 1200. Okay. And then ultimately, what? I want to do this square root. So when I do that, I find that the final velocity when it runs out of fuel is 87.63 when I say around it, 2.64 meters per second. Okay, so that was the final velocity when it runs out of fuel. Next part of the question. It says, How long does it take for it to run out of fuel? I&#x27;m gonna use the formula. Final velocity is acceleration times, time plus initial velocity. So the final blast me that I just solved for 87 0.64 is equal to 3.2 times time plus zero. And I find that the time for it to run out of fuel is 27.39 seconds. Okay, then the next part of the question, it wants to know the maximum altitude. Okay, so I know this velocity here is my 87. What&#x27;s 87.64? And I know this velocity is zero. I&#x27;m gonna try and figure out this displacement. Okay? So, again, using my formula, VF squared equals V. I squared plus two. A Delta X zero equals 87.64 squared. Plus two. Now, in this portion, acceleration. Um, forgot toe include that is 9.8 because we&#x27;re out of fuel now. It&#x27;s just acceleration due to gravity. And that&#x27;s pulling it down. A man. My displacement. That I don&#x27;t know. Okay, seven, When I solved for this, I find that the displacement from the point that the rocket runs out of fuel to the top of the peak is 300 and 91.84 meters. But it wants the total altitude. So don&#x27;t forget, we have to add on these 1200 meters as well. So the total altitude is 1591.84 meters. Okay, you can around your answer, however you want to about going to try and keep it as exact as possible. Okay, The next part of the question it wants to know how long it takes to reach the maximum altitude. So again, I&#x27;m gonna use the formula Final. The last G is acceleration times, time plus initial velocity. Okay, Now, again, our final velocity is zero. Acceleration is negative. 9.8 times time, plus our initial velocity Waas 87.64 Okay. And I find that the time for the portion where the rocket runs out of fuel. Um, to reach the peak is 8.94 seconds. But don&#x27;t forget, we have to add on the time, um that it took for the rocket to run out of fuel, which if you remember was 27.39 seconds. So the time to reach the peak is 36.33 seconds total. Okay, now, the next part of the question it is saying or it wants to know, Um, what is the velocity that the rocket strikes the earth with? So now we&#x27;re looking at the second half, and now I&#x27;m going to switch it up, I&#x27;m gonna say to make it easier on myself. I&#x27;m gonna now say that because everything&#x27;s moving in the downward direction. That down is positive now. Okay, So to figure out the velocity, um, here when it strikes the earth again, I&#x27;m gonna use This is my reference position with a velocity of zero. Okay, so again, the formula V f squared equals V. I squared. Plus two a Delta X final velocity. We don&#x27;t know the initial velocity was zero squared is zero plus two times 9.8 is my acceleration. Because again, its acceleration due to gravity times the displacement, which is my maximum altitude, which we found to be 1591.8 for and then we have to square root this. Okay, so we end up finding the final velocity with of the rocket hitting the earth is ah, 176.64 Or you could round it to 177 meters per second. But again, it&#x27;s in the downward direction, which is why I have a positive number. Because remember, I switched it. Everything in blue now, uh, positive is down. And then the final part of this question So wrapping it up the final part, it wants to know how long the rocket is in the air. So again, I&#x27;m gonna figure out the time it takes for the rocket to strike the earth again. Using the final equals 80 plus B I Okay, so 1 76.64 is equal to 9.8 T plus zero. So I find that time is 18.2 0 to 4. This is just to come down. Okay? Don&#x27;t forget. We need to add on the 36.33 seconds to go up. The pace of this is my down. This was the time that it took to go up, so whoops went a little too far. The total time ends up being 54 0.4 seconds

Nathan Silvano · Answer

Okay, So in this problem we have a rocket moving upwards. If our acceleration off to Ralph meters per second square, the rockets maintain his deceleration until he reaches the height off 29 meters. After this moment after disposition Hey, shut off his changing and continue its flight in free fall. Okay, so the first question is, what is the maximum height? Let&#x27;s go Ex Toto off the after rocket What is the maximum height that the rocket reaches? Okay, so first of all, let&#x27;s think about entire movement. Let&#x27;s see, we have our rocket moving from rest with acceleration of 12 meters per second squared. Then the rockets reaches first position. Ex ICO swan disposition. He shut offs his angel and continues moving upwards. And so he reaches a maximum height school ex too, and stop! The thing that we have to notice is that in this segment off the movement, his acceleration is the gravity&#x27;s acceleration off miners nine point 81. So actually we have two movements. The first movement is ah accelerated movement. And the 2nd 1 is a decelerated movement. So we need to use two equations to calculate it, each off them separately. Okay, so let&#x27;s calculate this. The first part of the movement is the accelerated move movement. So we want to find out the height. So let&#x27;s see, to calculate the maximum height, we need to discover the velocity. So, in the first part of the movements, we have these where it goes easier square. Well, us too. A doubt ex. Sorry. That&#x27;s call X one. So you guys can not get confused. This is going to be ex. What? Okay, so V, we don&#x27;t know. The zero is zero because he starts addressed, plus two times 12. And the first position we know is 29. So actually, the first velocity, the maximum velocity, it&#x27;s going to be 69 six. So the square root 696 It&#x27;s just 26.4 meters per second. So this is the first velocity. This is the velocity. A position X one. When we have the position X one, the final velocity, his 26 point for. Okay, so come back here. Now we have the velocity off the final position. We can just cover there. Position x two. So the position next to we&#x27;re going to use this immigration is just going to be the square equals to visit or square. Well, it&#x27;s true. G Delta Not doubt. That&#x27;s put ah X two in here x two. So let&#x27;s see. Their final velocity is your toe. The initial velocity is the fine of a lost such of the first part. So it&#x27;s just 69 Six miners, two times nine points. 81. It is the gravity&#x27;s acceleration now pointing downwards times the x two. Let&#x27;s get these X here. Okay, so let&#x27;s see the distance x two Just going to be, uh let&#x27;s see. 35 35 point 47 meters. So the answer to the first item, What is the maximum height that we call ext E X Toto? Just going to be x one plus x two. So this is finally 64 point 47 meters. This is the maximum height of the rockets. Okay, Next item the next item we need to calculate what is the speed of the rocket just before reaching the ground. Okay, so this time now we have 1/3 part of the movement. Let&#x27;s come back in here. See? Still rockets stop. Here we begin a turd art of the movement that is, the rockets beginning to fall under the gravity&#x27;s acceleration one to reach the ground. This is a free falling object. So in this part, off the movement, we can use again the same equation which are me to square because the zero less too times g Delta X So v zero is what we want to discover is your RV is what we want to discover Vizier is, you know, because in the beginning of the third part of the movement the beginning of the dirt art off their movement, the rocket starts from rest. So these ears just sooner. Plus two times nine point 81 Delta X Delta access the Toto space. The maximum height. It was just going to be 64 0.47. So calculating this, we have the answer to this second item. The velocity of the rocket just before reaching the ground is going to be dirty. Five point 57 meters per seconds. Okay, so the dirt item the eye can see we want to discover. I did told told oration off the rockets flights. So the total duration of the rockets fight we just need to use what information we have from the previous calculation. So we just need to use the vehicles, visit Europe, Loss 80. So let&#x27;s see. First of all, we need to calculate the time off each off their movements separately because you don&#x27;t have to. We don&#x27;t have a way to calculate it all the time. In one single calculation, we need to separate this movement. So the first part of the movement we start with initial velocity of zero with acceleration of 12. We need to find a time in the final velocity we know, which is. It&#x27;s just 96.4. So this is going to be 26.4. So their first time going to be 26.4 divided by 12. This is a code 2.2 seconds. The second part off their movement. We have another time. Vehicles 30 plus GT. This time we&#x27;re going to have V zero. V zero is 26.4 minors, 9.81 e. So the second time it&#x27;s going to be 26.4, divided by 9.81. This is just 2.7 seconds and the final part of the movement. They&#x27;re free. Falling from his maximum right height is just vehicles Visitor loss GT so V we already calculated this was 35 0.57 s is equal to zero plus 9.81 key. So the final time waas 35 point 57 divided by nine point 81. This is going to be equal to three points 62 seconds. So the answer to the final letter final writing is that total time it&#x27;s going to be to a point too. Plus 2.7 lost 3.62. This is going to be equal to eight point 52 seconds and this is the final answer to the problem. Thanks.

Ryan Hood · Answer

In order to calculate the average velocities, we&#x27;re going to need the velocity at the start in the end of the four point seven five second part. So if we assume that our initial losses zero when the rockets on the ground, we&#x27;re trying to solve for the final velocity after the one point one five seconds. So that will be our unknown. The time will be one point one five seconds and the distance traveled during the initial one point one five seconds is sixty three meters. Now we&#x27;re going to use the Kinnah Matic equation X minus X not is equal to one half be not plus b times t When were we plug in these values we get sixty three is equal to one half in this case be nada zero So that term goes away. So we&#x27;re just left with B times one point one five solving for the yields one hundred and nine point five seven meters per second. So this is the velocity at the beginning of the four point seven five second part. Now any of the velocity at the end of the four point seven five second part and to do this we&#x27;LL treat this velocity as the initial velocity and then calculate the new final velocity. So now Wien on is equal to one hundred nine point five seven meters per second. This is again are unknown. In this case, he is equal to four point seven five seconds and x minus X not is equal to a thousand minus sixty three because that&#x27;s the new distance traveled by the rocket during the four point seven five second. If it ends at a thousand and one sixty three the first time. Then it went the difference during the four point seven five second part. This is called a nine hundred three seven meters, and we&#x27;re going to use the same chromatic equation. X My sex night is equal to one half Levin on plus B comes T Nuria plug in so you get nine hundred thirty seven is equal to one half. Be not is now no longer. Zero. It&#x27;s one hundred nine point five seven plus V times four point seven five. Our unknown has B, and this is just an algebraic equation. At this point, solving it gives is equal to two hundred and eighty four point nine six meters per second and now we can actually start to calculate the things we need. Calculate. So for the four point seven five second part, the average velocity is the final velocity which is two hundred eighty four point nine six, Right, This guy minus the initial velocity which is one hundred nine point five seven when we divide. By the time that that took, which is four point seven five seconds and I get thirty six point nine two meters per second, I&#x27;m going to do the other part on the next page. So for part B, we need the full five point nine seconds, including the beginning of the takeoff and then the four point seven five second part. So for fool, five point nine seconds, the average Flossie is equal to the final velocity which is still two hundred eighty four point nine six. But now the initial velocity zero because originally have to be any of the five point nine six. It was moving at zero velocity and in the time it takes is five point nine seconds and what I get is forty eight point three meters per second, which is the answer to part me

Zachary Warner · Answer

for this question. We&#x27;re considering a rocket taking off on. We&#x27;re told that it travels a distance which I called D one of 63 meters and a time which I call t one of 1.15 seconds. We&#x27;re then told that after 4.75 more seconds so t to the rockets total distance traveled is 1000 meters. So d one plus d to is 1000 meters on Ben. T two is 4.75 seconds. So the total time to travel 1000 meters would be t one plus tea too. For part A were asked to find the average velocity. Um, there has to find the average velocity for the 4.75 2nd part of the flight or other words. In other words, for the tea to part of the flight. Well, the velocity for that part will call this Visa Bay. Since this is the velocity for part, A is going to be equal to the distance traveled for that part, which would be D too, right? So how do we find D too? Well, we just simply take our value of d one plus D two, which was 1000 meters and we subtract the one from that right And that would give us d too, which the one we know is 63 meters and this needs to be divided by the time it takes to travel that distance d to which was T too. So we plug our values into this expression. We find that this is 197 meters per second, which would give me which weaken boxing is our solution. For part a part B wants us to find the average velocity for the entire trip. Well, the average velocity for the entire trip will call this visa be. Since this is the lost he calculated in part, B is going to be equal to the distance traveled for the entire trip the one plus D to which we know is 1000 meters. Um, I didn&#x27;t mention this, but I converted kilometers into meters. We told we&#x27;re told it&#x27;s one kilometer which is equal to 1000 meters, and it&#x27;s gonna be divided by the time it takes to travel that distance which will be t one plus tea too. So if you notice the way the question worded it, it says for the 1st 5.9 seconds of the flight, but T one plus t two is 5.9 seconds. So that&#x27;s where I got t one plus tt from. So he plugged those guys into this expression and the Sequels. 169 meters per second. This could be boxed in is our solution for part B and that is the final part of this question.

Jayashree Behera · Answer

with a positive life. Tto be upwards now There are two periods off constant acceleration oneness A light to be 2.5 meters per seconds. Caf while the engines fire on then my acceleration will be negative 9.8 meters per second Scratch then the engines Shut it off on both of these arts accelerations are constant at during these times, so we can use constant acceleration in questions within each period. So basically during this period and this video now for the first part So they find a speak and hide at the end of the first 20 seconds, something is equal to during the seconds um, you will lose a right to be 2.5 minutes of the second. Scared two on initial velocity is Siegel fund. Initial height is also single. Now find the final velocity with loose the secretion. Since we have all the ban emitters on the wrist off the pan emitters to solve for rib eye. So we directly plugged them into this equation and we get this velocity to be 15 meters a second Mom for height, the videos this accretion over here because the same for the same reason we have all the perimeters needed to solve this equation. And we get this value of height or right to be 500 meter next considered awash in from this point, the maximum height. So for that we have I not could be 500 meter because ah, we&#x27;re starting from this point now. So now uh, why not will be 500 meters ve knocked. Lee will be not this than you. 15 meters per second on our maximum height Velocity zero. So vai is zero now and obviously acceleration is now negative 9.8 meters per second squared now we saw these equations to find the maximum height of it is why so yes, move to the next. It&#x27;s for that. So use desecration now Since we don&#x27;t have, they have no idea about the time taken to travel this distance. And we need to solve for heights of the secretions both at this also From this we can write why minus why not equal do this value and we solve this for the perimeters we have for the for the second motion on DH, This gives us 1 20 This means that divided the equal. Why not less one during the igniter on why Lord is as you can see, here is 500 meters So why will be 6 28 meter now the dietician off this part off the motion it is time could be found from This is a question the same that we used here I&#x27;m from here We can find an expression for time he solved it for the values we have on DH this time comes out, comes out to the 5.10 seconds the second But now at the highest point We know that velocity zero because ah, it comes to, ah moment that relate guns to arrest and then falls down again. But at that instant the Y issue on it why is obviously 9.8 meters per seconds downward And if you are taking positive, I access Toby upward. Then you can write a burrito. The negative nine point meter per second Scared Aziz We didn&#x27;t disgrace and the part But so consider the motion from the maximum height back to the ground. So we have Why not? Which is the maximum height And is he called the 6 28 meter? Because we are considering the motion from the maximum height. So the ground so final hide will be serial because it&#x27;s on the ground now off the city. Not why is here? Because at maximum, I, uh, thought it comes momentarily to arrest. So we&#x27;re not white. Is Siegel on? Obviously, acceleration is acceleration due to gravity of it is negative. 9.8 meter scare the negative sinus because it positive it points in the negative I direction. Now we will solve for this aggression and I appeal. And this will give us time. Basically, despite goes of it because we not buy you see it all now time will be equal toe twice off my minus. Why not over a guy and you have to take root over that because ofthe squared Come over here. He solved us and they find this timeto 11.3 seconds. So the total time off the rocket in air. This is quite a while. 20 seconds. Which is the stein? Less five point one serial seconds. That is the time taken by it to travel from this point. So jungle drums this point. So the maximum height. So this is the time plus time taken. Buy it toe. Come backto the ground from the maximum ID. So this time so we add them all on We get the total time it spends in air. So this is equal to 36.4 seconds on DH final velocities and it comes back with the ground just before it hits the ground. It is equality. So we solve. This equation is angry not quite of the seal a guy to be negative 9.8 meters squared and timeto element on three seconds like we just found out now. And this gives velocity to be negative on 13 meet up a second. So just before it hits the ground, the rocket will have a speed off 111 meters per second and off this little point in on the downward direction and therefore the negative science, which makes sense

Problem

If $x=3 a$ and $y=9 b,$ then all of the following…

Problem 9 Medium Difficulty

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